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Shingo Takemoto, Shunsuke Ono

This paper proposes a novel regularization method, named Spatio-Spectral Structure Tensor Total Variation (S3TTV), for denoising and destriping of hyperspectral (HS) images. HS images are inevitably contaminated by various types of noise, during acquisition process, due to the measurement equipment and the environment. For HS image denoising and destriping tasks, Spatio-Spectral Total Variation (SSTV), defined using second-order spatio-spectral differences, is widely known as a powerful regularization approach that models the underlying spatio-spectral properties. However, since SSTV refers only to adjacent pixels/bands, semi-local spatial structures are not preserved during denoising process. To address this problem, we newly design S3TTV, defined by the sum of the nuclear norms of matrices consisting of second-order spatio-spectral differences in small spectral blocks (we call these matrices as spatio-spectral structure tensors). The proposed regularization method simultaneously models the spatial piecewise-smoothness, the spatial similarity between adjacent bands, and the spectral correlation across all bands in small spectral blocks, leading to effective noise removal while preserving the semi-local spatial structures. Furthermore, we formulate the HS image denoising and destriping problem as a convex optimization problem involving S3TTV and develop an algorithm based on a preconditioned primal-dual splitting method to solve this problem efficiently.  Finally, we demonstrate the effectiveness of S3TTV by comparing it with existing methods, including state-of-the-art ones through denoising and destriping experiments.

本論文では，Spatio-Spectral Structure Tensor Total Variation (S3TTV) と名付けた新しいハイパースペクトル（HS）画像の混合ノイズ除去法を提案する．HS画像は，計測課程において，測定機器や環境に起因する様々な種類のノイズに汚染されることが避けられない．空間-スペクトル2次差分を用いて定義されるSpatio-Spectral Total Variation (SSTV) は，HS画像の基本的な空間-スペクトル特性をモデル化する強力な正則化アプローチとして，混合ノイズ除去を含め広く応用されている．しかし，SSTVは隣接する画像/バンドのみを参照するため，ノイズ除去課程で半局所的な空間構造が保持されない．この問題を解決するために，小さなスペクトルブロックにおける空間-スペクトル2次差分からなる行列（空間-スペクトル構造化行列と呼ぶ）の核ノルムの和として定義されるS3TTVを設計する．提案する正則化手法は，空間的な区分的滑らかさ，隣接バンド間の空間構造の類似性，全バンドにわたるスペクトル相関を同時にモデル化し，半局所的な構造を保持しながら効果的に混合ノイズを除去する．さらに，HS画像の混合ノイズ除去問題を，S3TTVを含む凸最適化問題として定式化する．そして，この問題を効率的に解くためのアルゴリズムを，ステップサイズ自動決定法付きの主-双対近接分離法に基づいて開発する．混合ノイズ除去の実験を通して，S3TTVを最先端のものを含む既存の手法と比較し，S3TTVの有効性を実証する．

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@misc{takemoto2024spatiospectral,

      title={Spatio-Spectral Structure Tensor Total Variation for Hyperspectral Image Denoising and Destriping}, 

      author={Shingo Takemoto and Shunsuke Ono},

      year={2024},

      eprint={2404.03313},

      archivePrefix={arXiv},

      primaryClass={eess.SP}

}

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